User-defined data types and operators in occam

This paper describes the addition of user-defined monadic and dyadic operators to occam* [1], together with some libraries that demonstrate their use. It also discusses some techniques used in their implementation in KRoC [2] for a variety of target machines

PASCAL/48 reference manual

PASCAL/48 is a programming language for the Intel MCS-48 series of microcomputers. In particular, it can be used with the Intel 8748. It is designed to allow the programmer to control most of the instructions being generated and the allocation of storage. The language can be used instead of ASSEMBLY language in most applications while allowing the user the necessary degree of control over hardware resources. Although it is called PASCAL/48, the language differs in many ways from PASCAL. The program structure and statements of the two languages are similar, but the expression mechanism and data types are different. The PASCAL/48 cross-compiler is written in PASCAL and runs on the CDC CYBER NOS system. It generates object code in Intel hexadecimal format that can be used to program the MCS-48 series of microcomputers. This reference manual defines the language, describes the predeclared procedures, lists error messages, illustrates use, and includes language syntax diagrams

Manipulation of expressions in a relational algebra

This paper describes a syntax for expressions based on the relational algebra. A tree representation is generated when an expression is analyzed. Transformations on the tree representations of expressions are applied in order to obtain improvements with respect to the speed of evaluation in a data base environment

Type classes for efficient exact real arithmetic in Coq

Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the computer handles the error estimates. Previously, we [Krebbers/Spitters 2011] provided a fast implementation of the exact real numbers in the Coq proof assistant. Our implementation improved on an earlier implementation by O'Connor by using type classes to describe an abstract specification of the underlying dense set from which the real numbers are built. In particular, we used dyadic rationals built from Coq's machine integers to obtain a 100 times speed up of the basic operations already. This article is a substantially expanded version of [Krebbers/Spitters 2011] in which the implementation is extended in the various ways. First, we implement and verify the sine and cosine function. Secondly, we create an additional implementation of the dense set based on Coq's fast rational numbers. Thirdly, we extend the hierarchy to capture order on undecidable structures, while it was limited to decidable structures before. This hierarchy, based on type classes, allows us to share theory on the naturals, integers, rationals, dyadics, and reals in a convenient way. Finally, we obtain another dramatic speed-up by avoiding evaluation of termination proofs at runtime.Comment: arXiv admin note: text overlap with arXiv:1105.275

A C++11 implementation of arbitrary-rank tensors for high-performance computing

This article discusses an efficient implementation of tensors of arbitrary rank by using some of the idioms introduced by the recently published C++ ISO Standard (C++11). With the aims at providing a basic building block for high-performance computing, a single Array class template is carefully crafted, from which vectors, matrices, and even higher-order tensors can be created. An expression template facility is also built around the array class template to provide convenient mathematical syntax. As a result, by using templates, an extra high-level layer is added to the C++ language when dealing with algebraic objects and their operations, without compromising performance. The implementation is tested running on both CPU and GPU.Comment: 21 pages, 6 figures, 1 tabl

Visual Programming Language for Tacit Subset of J Programming Language

Visual programming is the idea of using graphical icons to create programs. I take a look at available solutions and challenges facing visual languages. Keeping these challenges in mind, I measure the suitability of Blockly and highlight the advantages of using Blockly for creating a visual programming environment for the J programming language. Blockly is an open source general purpose visual programming language designed by Google which provides a wide range of features and is meant to be customized to the user’s needs. I also discuss features of the J programming language that make it suitable for use in visual programming language. The result is a visual programming environment for the tacit subset of the J programming language

JMSL - a language derived from APL

A new AFL-derived language called JMSL is presented which rnodifies seven aspects of APL so that many current and potential APL users could benefit from a language which is easier to learn, read, write, and maintain. JMSL uses ASCII tokens instead of APL symbols to remedy interfacing, extensibility, and readability problems with APL. JMSL revises and extends APL built-in capabilities to provide greater expression and improved symbol-meaning correspondence. JMSL includes a new notation for nested arrays (a powerful data structure which combines the array processing of APL with the tree processing of LISP). JMSL provides hierarchical directories (similar to PASCAL or PL/I records) to allow structures to be indexed by name. JMSL modifies the traditional APL library/workspace storage interface by unifying the syntax of system commands in a way which allows UNIX-like directory storage. JMSL provides high-level control structures similar to those found in block-structured languages, including an event-handling mechanism. JMSL amends the APL scope rules to alleviate problems with side effects and object localization. Some areas of future work are discussed, and a description of JMSL syntax and semantics is included

Type inference for linear algebra with units of measurement

Refining types of numerical data with units of measurement has the potential to increase safety of programming languages but is restricted to homogeneous units when checked statically with parametric polymorphism. We lift units to vectors and show how type inference of linear algebra expressions can statically determine safety for data with heterogeneous units. The typing is based on the dyadic product of units that is found in linear transformations and the corresponding vector spaces. Since it is a refinement of Kennedy’s types for units we automatically obtain a unification algorithm, which gives principal types for linear algebra. The extension of unit-unification to numerical data with heterogeneous units makes the safety of statically checked numerical expressions available to a significantly larger set of use-cases

Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories

The computer-mechanization of an ambitious explicit ethical theory, Gewirth's Principle of Generic Consistency, is used to showcase an approach for representing and reasoning with ethical theories exhibiting complex logical features like alethic and deontic modalities, indexicals, higher-order quantification, among others. Harnessing the high expressive power of Church's type theory as a meta-logic to semantically embed a combination of quantified non-classical logics, our work pushes existing boundaries in knowledge representation and reasoning. We demonstrate that intuitive encodings of complex ethical theories and their automation on the computer are no longer antipodes.Comment: 14 page

Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support

A framework and methodology---termed LogiKEy---for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples---all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure